Packs of playing cards comprising fifty-two cards, each denoting a different value of one of four suits (clubs, diamonds, hearts, and spades) and herein referred to as a standard deck, have a long and ancient history. In the past there have been numerous proposals for variations in the standard deck. A known alteration in the standard deck has been to provide a deck of cards in which each individual card represents more than one value, as indicated on its front face.
For example, U.S. Pat. No. 821,781 (Cadwallader, May 29, 1906) describes a deck of cards, each with two values. The two values were designed so that they could be distinguished as either major or subordinate suits.
U.S. Pat. De. No. 118,977 (Kermode, Feb. 13, 1940) shows a deck of fifty-five cards comprised of front faces partially occupied by a domino representation, a letter of the alphabet, and a standard playing card marking.
U.S. Pat. De. No. 212,239 (Schick, Sept. 17, 1968) shows an ornamental design for a standard deck of playing cards with two values each.
U.S. Pat. De. No. 222,490 (Alaska, Oct. 26, 1971) shows a standard deck of cards which are split into two values across the middle by means of transparent/opaque layers in each half.
U.S. Pat. No. 4,170,358 (Hancock, Oct. 9, 1979) shows another two-valued standard deck of cards which was an improvement on the prior art. The Hancock patent cites many other examples of two-valued cards known in the prior art. Hancock notes that none of the packs of split playing cards has achieved widespread acceptance, dispite their apparent offering of increased ranges of card playing possibilities. In most cases, the arrangement of the two zones on the split cards of the prior art renders the decks difficult and confusing to read and play. The preferred embodiment of the Hancock patent is to yield a pack of cards which essentially comprises two standard decks; a major suit deck and a minor suit deck, whereby each individual deck is designed to be distinctly substantiated from the other deck as indicated by various shadings or colors.
It is important to note that Hancock uses each value only twice, therefore limiting the number of combinations obtainable. There is an almost random coupling of the two values which appear on each card. The specific couplings of suit/value pairs on an individual card have been inappropriate from a statistical point of view, resulting in yet another deck of two value cards which has not achieved widespread acceptance, since it is apparently unsatisfactory in play. Two value cards of the prior art have not constituted fair games when used in play.
A fair game shall be considered one in which the probabilities of any given hand can be predetermined so that successful winning strategies can be developed. With a standard deck, for example, a poker hand of four of a kind beats a full house because the probability of being dealt four of a kind is less than the probability of being dealt a full house. The more difficult the hand, the greater its rank. This holds true for any standard deck, and can be readily predetermined using the correct mathematical probability counting techniques. Since all standard decks are the same, the rules of all card games are the same for all standard decks. Hence standard decks result in fair games.
In the two-valued standard decks of the prior art, an inadequacy in the development of these decks neglects consistency in the probabilities of any given game in which the two standard decks are considered in play simultaneously. Thus the two-value decks of the prior art do not constitute fair games. A somewhat rigorous mathematical explanation seems necessary. The following definition is required: the number of subsets, each of size `r`, that a set with `n` elements has is called the number of combinations of `n` things `r` at a time and is denoted by ##EQU1## Mathematically, ##EQU2## It should be noted that the order of things is not important (ex: 1,2,3=1,3,2=3,2,1, etc.).